DIAGNOSIS The thermostat is not receiving sufficient power from your HVAC system's C-wire. The Amazon Smart Thermostat requires a continuous 24V AC power source.
FIX Verify your wiring. Remove the thermostat faceplate. Confirm a wire is connected to the C terminal on the wall plate. If no C-wire is present, you must use the included power extender kit. Install the power extender kit module at your furnace/air handler, not at the thermostat.
IF THAT DIDN'T WORK Check the furnace/air handler's 3A fuse. A blown fuse on the control board will cut all power. Locate and inspect the small, clear, glass 3A fuse on the HVAC control board. Replace it if the internal wire is broken.
HEADS UP Do not attempt to use the G-wire as a substitute for the C-wire. This is a common incorrect wiring hack that can damage the thermostat or HVAC fan control.